The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in general difficult to determine exact values. Many unknotting numbers can be determined from a knot's knot signature. A knot with unknotting number 1 is a prime knot. It is not always true that the unknotting number is achieved in a projection with the minimal number of crossings.

algebraic unknotting number | Bennequin's conjecture | knot signature | Milnor's conjecture | slice-Bennequin inequality